Maximal $\textrm {PSL}_2$ Subgroups of Exceptional Groups of Lie Type, David A. Craven

Автор: Alastair J. Litterick
Название: On Non-Generic Finite Subgroups of Exceptional Algebraic Groups
ISBN: 1470428377 ISBN-13(EAN): 9781470428372
Издательство: Mare Nostrum (Eurospan)
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Цена: 77610.00 T
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Описание: The study of finite subgroups of a simple algebraic group $G$ reduces in a sense to those which are almost simple. If an almost simple subgroup of $G$ has a socle which is not isomorphic to a group of Lie type in the underlying characteristic of $G$, then the subgroup is called non-generic. This paper considers non-generic subgroups of simple algebraic groups of exceptional type in arbitrary characteristic.

Автор: John Guaschi; Daniel Juan-Pineda; Silvia Mill?n L?
Название: The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)
ISBN: 3319994883 ISBN-13(EAN): 9783319994888
Издательство: Springer
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Цена: 51230.00 T
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Описание: This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory. Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.

Автор: Deserti, Julie
Название: Cremona group and its subgroups
ISBN: 1470460122 ISBN-13(EAN): 9781470460129
Издательство: Mare Nostrum (Eurospan)
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Цена: 104500.00 T
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Описание: The goal of this book is to present a portrait of the $n$-dimensional Cremona group with an emphasis on the 2-dimensional case. After recalling some crucial tools, the book describes a naturally defined infinite dimensional hyperbolic space on which the Cremona group acts.This space plays a fundamental role in the study of Cremona groups, as it allows one to apply tools from geometric group theory to explore properties of the subgroups of the Cremona group as well as the degree growth and dynamical behavior of birational transformations. The book describes natural topologies on the Cremona group, codifies the notion of algebraic subgroups of the Cremona groups and finishes with a chapter on the dynamics of their actions.This book is aimed at graduate students and researchers in algebraic geometry who are interested in birational geometry and its interactions with geometric group theory and dynamical systems.

Автор: R. Lawther
Название: Maximal Abelian Sets of Roots
ISBN: 147042679X ISBN-13(EAN): 9781470426798
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: In this work the author lets $\Phi$ be an irreducible root system, with Coxeter group $W$. He considers subsets of $\Phi$ which are abelian, meaning that no two roots in the set have sum in $\Phi \cup \{ 0 \}$. He classifies all maximal abelian sets up to the action of $W$: for each $W$-orbit of maximal abelian sets we provide an explicit representative $X$.

Автор: Madabusi S. Raghunathan
Название: Discrete Subgroups of Lie Groups
ISBN: 3642864287 ISBN-13(EAN): 9783642864285
Издательство: Springer
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Цена: 111790.00 T
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Описание: Our interest, by and large, is in a special class of discrete subgroups of Lie groups, viz., lattices (by a lattice in a locally compact group G, we mean a discrete subgroup H such that the homogeneous space GJ H carries a finite G-invariant measure). It is assumed that the reader has considerable familiarity with Lie groups and algebraic groups.

Автор: Ragnar-Olaf Buchweitz
Название: Maximal Cohen-Macaulay Modules and Tate Cohomology
ISBN: 1470453401 ISBN-13(EAN): 9781470453404
Издательство: Mare Nostrum (Eurospan)
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Цена: 104500.00 T
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Описание: This book is a lightly edited version of the unpublished manuscript Maximal Cohen-Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen-Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen-Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Автор: Joseph Kirtland
Название: Complementation of Normal Subgroups: In Finite Groups
ISBN: 311047879X ISBN-13(EAN): 9783110478792
Издательство: Walter de Gruyter
Цена: 107790.00 T
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Описание:

Starting with the Schur-Zassenhaus theorem, this monograph documents a wide variety of results concerning complementation of normal subgroups in finite groups. The contents cover a wide range of material from reduction theorems and subgroups in the derived and lower nilpotent series to abelian normal subgroups and formations.